2.1778   ODE No. 1778

\[ y(x)^2 y''(x)-a=0 \] Mathematica : cpu = 0.238176 (sec), leaf count = 65


\[\text {Solve}\left [\left (\frac {y(x) \sqrt {-\frac {2 a}{y(x)}+c_1}}{c_1}+\frac {2 a \tanh ^{-1}\left (\frac {\sqrt {-\frac {2 a}{y(x)}+c_1}}{\sqrt {c_1}}\right )}{c_1{}^{3/2}}\right ){}^2=(x+c_2){}^2,y(x)\right ]\] Maple : cpu = 1.525 (sec), leaf count = 245


\[y \relax (x ) = \frac {c_{1} \left (c_{1} a +{\mathrm e}^{\RootOf \left (\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2}-2 \textit {\_Z} c_{1}^{3} a \,{\mathrm e}^{\textit {\_Z}}-\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}} c_{1}^{2}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}} c_{2}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}} x \right )}\right )^{2} {\mathrm e}^{-\RootOf \left (\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2}-2 \textit {\_Z} c_{1}^{3} a \,{\mathrm e}^{\textit {\_Z}}-\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}} c_{1}^{2}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}} c_{2}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}} x \right )}}{2}\]